Time, reduced

Fig. 3. Composite curve of tme stress at break at 40°C vs reduced time to break tjfor polypropylene fibers of three draw ratios (15) (—...

Variable Variable ft e t/t, reduced time, fraction of surface covered by adsorbed ... 

The chief quantities based on tracer tests are summarized in Table 23-4. Effluent concentrations resulting from impulse and step inputs are designated Cg and C , respectively. The initial mean concentration resulting from an impulse of magnitude m into a vessel of volume is C = mfVr- The mean residence time is the ratio of the vessel volume to the volumetric flow rate, t = V fV or t = jo tCg dt/jo Cg dt. The reduced time is t = t/t. 

Thus, it is shown, that use of ultrasonic at the stage of sample preparation or different type soils allows considerably to reduce time of extracts obtaining for determination of soil forms of heavy metals and realization of full decomposing for an estimation of the gross contents. 

Our researches of a method fire assay (FA) of ores have shown that the losses of noble metals (NM) in scoria s FA hardly depend on composition of used fusion mixture. Usage of ultrasonic (US) oscillations of low frequency allows lowering on 50-100° temperature FA, to reduce time in 3-4 times. Even under unfavorable conditions thus the extent of extraction NM is conserved at FA on NiS (Ni S ) or Sn and is augmented at usage as a collector Pb or Cu. 

Faster product development and reduced time to market... 

These are commonly presented graphically as fractional recovered strain against log (reduced time) curves as typified in Figure 9.11. In the case of the acetal... 

Upon integrating and expressing time in terms of the reduced time r = 1 IT, one finds... 

The second dimensionless variable is called the Reduced Time, tg, defined as... 

Extensive tests have shown that if the final creep strain is not large then a graph of Fractional Recovery against Reduced Time is a master curve which... 

However, kAdt = dr because kA isaninversetimeconstantassociatedwiththerateofthe firstchemicalreactionandr is"reduced" time.Thisgivesusthefollowingthreeequations ... 

An alternative intervention would be to make the procedures ideal (rating = 9). Changing the ratings for procedures to this value for each task (instead of reducing time stress) produces the following results. 

Grace [18] evaluated t% as a function of 8 for viscoelastic matrices. His results are shown in Fig. 10. The reduced time increases as the viscosity ratio increases. If the residence time during a processing is less than... 

Some evolution types observed in our simulations are shown in Figs. 2-7. The simulations were performed for the same 2D alloy model as that used in Refs. , on a square lattice of 128x128 sites with periodic boundary conditions. The as-quenched distribution Ci(0) was characterized by its mean value c and small random fluctuations Sci = 0.01. The intersite atomic jumps were supposed to occur only between nearest neighbors and we used the reduced time variable t = <7,m-... 

Fig. 12. Temporal evolution of q = cf (upper row) and c- (lower row) for the alloy model described in text, at T = 0.4, c = 0.35, = 0.01, and following values of the reduced time...

The complexity and reduced time constants of modern processes imply the adoption of high performance programmable controllers. This requires not only higher processing speed but also more advanced control algorithms that can optimize the process operation in real time. 

Characteristic features of a—time curves for reactions of solids are discussed with reference to Fig. 1, a generalized reduced-time plot in which time values have been scaled to t0.s = 1.00 when a = 0.5. A is an initial reaction, sometimes associated with the decomposition of impurities or unstable superficial material. B is the induction period, usually regarded as being terminated by the development of stable nuclei (often completed at a low value of a). C is the acceleratory period of growth of such nuclei, perhaps accompanied by further nucleation, and which extends to the... 

Mcllvried and Massoth [484] applied essentially the same approach as Hutchinson et al. [483] to both the contracting volume and diffusion-controlled models with normal and log—normal particle size distributions. They produced generalized plots of a against reduced time r (defined by t = kt/p) for various values of the standard deviation of the distribution, a (log—normal distribution) or the dispersion ratio, a/p (normal distribution with mean particle radius, p). 

Fig. 2. Reduced time plots for the Avrami—Erofe ev equation [eqn. (6)] with n = 2, 3 and 4 and tT = (t/ta.g) the Prout—Tompkins expression [eqn. (9)] is included as the broken line.

Fig. 3. Reduced time plots, tr = (t/t0.9), for the contracting area and contracting volume equations [eqn. (7), n = 2 and 3], diffusion-controlled reactions proceedings in one [eqn. (10)], two [eqn. (13)] and three [eqn. (14)] dimensions, the Ginstling— Brounshtein equation [eqn. (11)] and first-, second- and third-order reactions [eqns. (15)—(17)]. Diffusion control is shown as a full line, interface advance as a broken line and reaction orders are dotted. Rate processes become more strongly deceleratory as the number of dimensions in which interface advance occurs is increased. The numbers on the curves indicate the equation numbers.

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